Problem: Simplify the following expression: ${-5(4z+9)-(-3+9z)}$
Solution: Distribute the ${-5}$ into the first set of parentheses: $ {-5(}\gray{4z+9}{)} - (-3+9z) $ $ {-20z-45} - (-3+9z) $ The minus sign in front of the parentheses means we multiply each term inside the parentheses by ${-1}$ $ -20z-45 {-1(}\gray{-3+9z}{)} $ $ -20z-45 + {3-9z} $ Rewrite the expression to group the ${z}$ terms and numeric terms: $ {-20z - 9z} {-45 + 3}$ Combine the ${z}$ terms: $ {-29z} {-45 + 3}$ Combine the numeric terms: $ {-29z} {-42}$ The simplified expression is $-29z-42$